A circle has a circumference of $18\pi$. It has an arc of length $8\pi$. What is the central angle of the arc, in degrees? ${18\pi}$ ${160^\circ}$ $\color{#DF0030}{8\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{s}{c}$ $\dfrac{\theta}{360 ^ \circ} = 8\pi \div 18\pi$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{4}{9}$ $\theta = \dfrac{4}{9} \times 360 ^ \circ$ $\theta = 160^\circ$